In this paper, we construct two classes of permutation polynomials over finite fields. First, by one well-known lemma of Zieve, we characterize one class permutation polynomials of the finite field, which generalizes ...In this paper, we construct two classes of permutation polynomials over finite fields. First, by one well-known lemma of Zieve, we characterize one class permutation polynomials of the finite field, which generalizes the result of Marcos. Second, by using the onto property of functions related to the elementary symmetric polynomial in multivariable and the general trace function, we construct another class permutation polynomials of the finite field. This extends the results of Marcos, Zieve, Qin and Hong to the more general cases. Particularly, the latter result gives a rather more general answer to an open problem raised by Zieve in 2010.展开更多
A class of new PN sequence with prime number periods of 4t +1 form (t is an integer)is constructed.The advantage of these PN sequencs over the m(M) sequence is their large number of alternative periods.They hav...A class of new PN sequence with prime number periods of 4t +1 form (t is an integer)is constructed.The advantage of these PN sequencs over the m(M) sequence is their large number of alternative periods.They have good pseudo random characteristics demonstrated by the expression of periodic autocorrelation function found out in this paper.展开更多
Pseudo-random sequences with long period, low correlation, high linear complexity, and uniform distribution of bit patterns are widely used in the field of information security and cryptography. This paper proposes an...Pseudo-random sequences with long period, low correlation, high linear complexity, and uniform distribution of bit patterns are widely used in the field of information security and cryptography. This paper proposes an approach for generating a pseudo-random multi-value sequence (including a binary sequence) by utilizing a primitive polynomial, trace function, and k-th power residue symbol over the sub extension field. All our previous sequences are defined over the prime field, whereas, proposed sequence in this paper is defined over the sub extension field. Thus, it’s a new and innovative perception to consider the sub extension field during the sequence generation procedure. By considering the sub extension field, two notable outcomes are: proposed sequence holds higher linear complexity and more uniform distribution of bit patterns compared to our previous work which defined over the prime field. Additionally, other important properties of the proposed multi-value sequence such as period, autocorrelation, and cross-correlation are theoretically shown along with some experimental results.展开更多
Several kinds of stream ciphers—complementary sequences of period sequences,partial sum of period sequences,inverse order sequences and finitely generated sequences,arestudied by using techniques of generating functi...Several kinds of stream ciphers—complementary sequences of period sequences,partial sum of period sequences,inverse order sequences and finitely generated sequences,arestudied by using techniques of generating functions.Their minimal polynomials,periods,as wellas generating functions are given.As to finitely generated sequences,the change of their linearcomplexity profiles as well as the relationship between the two generated sequences usder thecase in which the degree of connected polynomials are fixed,are discussed.展开更多
In 1984, R. A. Scholtz and L. R. Welch constructed a series of new binary se-quences which are called GMW sequences by using the trace function as follows: LetM, J be positive integers, J|M, α be a primitive element ...In 1984, R. A. Scholtz and L. R. Welch constructed a series of new binary se-quences which are called GMW sequences by using the trace function as follows: LetM, J be positive integers, J|M, α be a primitive element of the finite field GF（2<sup>M</sup>）, rbe a positive integer, 1≤r≤2<sup>J</sup>, and（r, 2<sup>J</sup>-1）=1. Then the sequence b=b（0）b（1）…b（n）…is called GMW sequence over GF（2）. Here b（n）=tr<sub>1</sub><sup>J</sup>（tr<sub>J</sub><sup>M</sup>α<sup>n</sup>）<sup>r</sup>, for n=0, 1, 2….展开更多
基金Supported by the Research Initiation Fund for Young Teachers of China West Normal University(412679)
文摘In this paper, we construct two classes of permutation polynomials over finite fields. First, by one well-known lemma of Zieve, we characterize one class permutation polynomials of the finite field, which generalizes the result of Marcos. Second, by using the onto property of functions related to the elementary symmetric polynomial in multivariable and the general trace function, we construct another class permutation polynomials of the finite field. This extends the results of Marcos, Zieve, Qin and Hong to the more general cases. Particularly, the latter result gives a rather more general answer to an open problem raised by Zieve in 2010.
文摘A class of new PN sequence with prime number periods of 4t +1 form (t is an integer)is constructed.The advantage of these PN sequencs over the m(M) sequence is their large number of alternative periods.They have good pseudo random characteristics demonstrated by the expression of periodic autocorrelation function found out in this paper.
文摘Pseudo-random sequences with long period, low correlation, high linear complexity, and uniform distribution of bit patterns are widely used in the field of information security and cryptography. This paper proposes an approach for generating a pseudo-random multi-value sequence (including a binary sequence) by utilizing a primitive polynomial, trace function, and k-th power residue symbol over the sub extension field. All our previous sequences are defined over the prime field, whereas, proposed sequence in this paper is defined over the sub extension field. Thus, it’s a new and innovative perception to consider the sub extension field during the sequence generation procedure. By considering the sub extension field, two notable outcomes are: proposed sequence holds higher linear complexity and more uniform distribution of bit patterns compared to our previous work which defined over the prime field. Additionally, other important properties of the proposed multi-value sequence such as period, autocorrelation, and cross-correlation are theoretically shown along with some experimental results.
文摘Several kinds of stream ciphers—complementary sequences of period sequences,partial sum of period sequences,inverse order sequences and finitely generated sequences,arestudied by using techniques of generating functions.Their minimal polynomials,periods,as wellas generating functions are given.As to finitely generated sequences,the change of their linearcomplexity profiles as well as the relationship between the two generated sequences usder thecase in which the degree of connected polynomials are fixed,are discussed.
文摘In 1984, R. A. Scholtz and L. R. Welch constructed a series of new binary se-quences which are called GMW sequences by using the trace function as follows: LetM, J be positive integers, J|M, α be a primitive element of the finite field GF（2<sup>M</sup>）, rbe a positive integer, 1≤r≤2<sup>J</sup>, and（r, 2<sup>J</sup>-1）=1. Then the sequence b=b（0）b（1）…b（n）…is called GMW sequence over GF（2）. Here b（n）=tr<sub>1</sub><sup>J</sup>（tr<sub>J</sub><sup>M</sup>α<sup>n</sup>）<sup>r</sup>, for n=0, 1, 2….
